Runoff Approval Ranking?

Do you know if there is such a method:

Voting form
The voter classifies only his favorite candidates, even with equal positions, ex:
[1st, 1st, 2nd, 3rd, -, -, -, -]
First round
All votes are considered as approval voting, like this: [1,1,1,1,0,0,0,0]
The candidate with the highest sum of points is the 1st winner.
The votes are added up again, excluding the votes that had supported the 1st winner.
The candidate who now obtains the highest sum of points is the 2nd winner.
Round two
Of the two winners of the first round, the one who outweighs the other the most times, wins.

It can also be done with range, removing the points given to the first winner from all the candidates by one vote (compared to STAR it resists clones, and reduces the tactic in which maximum points are given to all candidates).

I vaguely recall something called “TTR-EX Score/STAR” or something like that, which is fairly similar to your idea and used to be discussed on r/EndFPTP by u/BothBawlz and u/curiouslefty. I’ll update this comment if I find it.

I looked through his comments, but it does not seem to me that he indicated the main feature of the system that I proposed, that is:
eliminate the points of the first winner from all the other candidates, in each single vote, before making the sum to find the second winner.

This is a similar mechanism to that of Sequentially Spent Score. Of course I realize that you do not want to do surplus handling in your mechanism because you want to exhaust as much of fist group as possible. The spending mechanic is similar though.

In principle doing a STAR like thing where you take the top two winners from a PR system seems like an interesting idea. This is immune to clones which is one criticism of traditional STAR. I’ll let you know if I come up with any flaws with this. It might be prone to polarization…

If you add this mechanism to the new STAR, you also eliminate the problem of clones, and I would say that it becomes quite an excellent method.
I could consider him a worthy opponent of the DV (for single winner) given its simplicity.

Maybe you’re right in saying that there may be polarization like:
I award 10 points to my most favorite candidates (A), 1 point to the other least favorite candidates (B), and 0 points to all the disapproved candidates (C ).
Ex: [10,10,1,1,1,0,0,0]
In this way:

(1) if A wins first, the others go to 0 points. Ok (avoid clones of A).
(2) if B wins first, A still has 9 points and could win second. Ok.
(3) if C wins first, the vote remains unchanged. Ok.
(4) if A-B or A-C win 1st round, A will always be very favored. Ok.
(5) if B-C win 1st round, B will be favored to the maximum against C. Ok.
(6) If 2 equal candidates win (A-A, B-B, C-C) the vote become null. Not Ok, but acceptable in this case.

Voting in that way, it seems that there is no negative side, if instead the points of B were more than 1, there would be damages in cases (2) and (4, A-B), but improvements in (6).

This tactic seems to me a form of Bullet Voting.
With the clone management indicated by me, this tactic increases (due to point 2) but at least the big problem of the clones is avoided (point 1).
Without the clone management indicated by me, this tactic is increases by the point (4, A-B), and reduce by the point (1).

The polarization is likely more of an issue than clones. STAR will never do worse than score so it is “bounded” by a good system.

The polarization comes from not doing surplus handling. RRV does not require surplus handling. What about top two from RRV?

Maybe there is a way to combine RRV selection with IRNR normalization to simplify the process… it would be way too complicated to do it with both for a single winner.

Okay, my last criticism isn’t about polarization, but it’s still valid.

If in a vote like this: A[10] B[10] C[0], A is the 1st winner, then not reducing the points of B to 0 always generates a bit the problem of clones in the context of a single winner (beyond to the tactic where 10 points are given to all the favorites).
In my opinion, RRV it makes sense but only for multiple winners.

The problem is that my latest criticism doesn’t hit the STAR, so maybe STAR is better than “new STAR”.

If by “new STAR” you mean the one you proposed in this thread then I agree. However, I think that the IRNR normalization is better than the marjoritarian one.

With “new STAR” I refer only to the use of IRNR normalization.
Between Bullet Voting (new STAR) and marjoritarian (STAR), I don’t know what’s worse.